Relativistic Corrections to the Exclusive Decays of C-even Bottomonia into S-wave Charmonium Pairs

Details Relativistic Corrections to the Exclusive Decays of C-even Bottomonia into S-wave Charmonium Pairs Relativistic Corrections to the Exclusive Decays of C-even Bottomonia into S-wave Charmonium Pairs

2011-08-20

arxiv.org/abs/1108.4104v2

Phys. Rev. D 84, 074026 (2011)

Physics

High Energy Physics

High Energy Physics - Phenomenology

20 pages, 1 figure. Typos corrected, published version

Scientific paper

Within the nonrelativistic quantum chromodynamics (NRQCD) factorization formalism, we compute the relativistic corrections to the exclusive decays of bottomonia with even charge conjugation parity into $S$-wave charmonium pairs at leading order in the strong coupling constant. Relativistic corrections are resummed for a class of color-singlet contributions to all orders in the charm-quark velocity $v_c$ in the charmonium rest frame. Almost every process that we consider in this work has negative relativistic corrections ranging from -20 to -35,%. Among the various processes, the relativistic corrections of the next-to-leading order in $v_c$ to the decay rate for $\chi_{b2}\to \eta_c(mS)+\eta_c(nS)$ with $m,$ $n=1$ or 2 are very large. In every case, the resummation of the relativistic corrections enhances the rate in comparison with the next-to-leading-order results. We compare our results with available predictions based on the NRQCD factorization formalism. The NRQCD predictions are significantly smaller than those based on the light-cone formalism by an or two orders of magnitudes.

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